Question

The difference of squares of two numbers is 180.
the square of the smaller number is 8 times the larger number. Find the two numbers.

Answer 1

Answer:

We have,

Let the large number is =x

Square of smaller number is =8x

Now, According to given question,

x 2 −8x=180

⇒x 2 −8x−180=0

⇒x 2−(18−10)x−180=0

⇒x 2 −18x+10x−180=0

⇒x(x−18)+10(x−18)=0

⇒(x−18)(x+10)=0

⇒x−18=0,x+10=0

⇒x=18,x=−10

⇒x=−10,18

Either

x=−10 and x=18

x=18 is true (Positive value)

Now, square of small number

=18x=18×8=144

144

=12

Hence, this is the answer.

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Answer 2

Question:

The difference of squares of two numbers is 180.

the square of the smaller number is 8 times the larger number. Find the two numbers.

Answer:

The two numbers are 18 and 12

Explanation:

• Let the larger and smaller number be X and y respectively.

According to the question,

REFER TO THE ATTACHMENT PLS

However, largest side cannot be negative as 8 times of larger number will be negative. Hence, square of smaller number will be negative which is not possible.

Therefore,

Larger number= 18

X=18

So,y^2= 8x

y^2=8×18

y^2=144

y=√144

y=12

The two numbers are 18 and 12

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